Andrey L. Targonskii, On the One Extremal Problem with the Free Poles on the Unit Circle, IJARM Volume 6, International Journal of Advanced Research in Mathematics (Volume 6) https://www.scipress.com/IJARM.6.26 Abstract: The sharp estimates of the product of the inner radius for pairwise disjoint domains are obtained. In particular, we solve an extremal problem in the case of an arbitrary finite number of the free poles on the unit circle for the following functional (see formula in paper) Keywords: Green Function, Inner Radius of Domain, Logarithmic Capacity, Piecewise-Separating Transformation, Quadratic Differential, Radial Systems of Points, Variational Formula